Determination of one-centre core integrals from the average energies of atomic configurations

One-center core integrals for valence orbitals are determined from the experimental average energies of neutral atomic configurations from Li through Zn. These values are compared with those estimated from CNDO /1, “INDO /1”, CNDO /2, “INDO /2” and with theoretical values calculated from a pseudo-potential method. The agreement is good between values obtained from neutral atoms and from the psuedo-potential calculation except for the 3d orbitals of the transition elements where the theoretically calculated integrals over single ξ functions are not realistic. These two methods reproduce both term and average configuration energies for the first two rows of atoms; the semiempirical method reliably reproduces them for the third row. The CNDO /1 and INDO /1 methods underestimate atomic energies, while the CNDO /2 and INDO /2 procedures fail rather poorly. The propriety of using core integrals estimated semiempirically in molecular orbital calculations is discussed.     

Functional dependence of core-excitation energies

We examine in depth the functional dependence of computed core-electron binding and excitation energies based on a total-energy difference approach within Kohn-Sham density functional theory. Twenty-seven functional combinations were studied using a database of reliable experimental data on 18 molecules. The computed core-electron binding energies are largely dependent on the choice of exchange functional. The term value of the first resonant excited state and energy differences between the lowest core-excited states are, however, quite insensitive to the choice of functionals since the errors due to the core-region cancel out. Using these results we define a different exchange functional, which mixes two functionals designed by Perdew and Wang (PD86 and PD91), with the best results for both excitation and binding energies obtained for a mixing ratio 60:40 between these. We also reexamine the relativistic corrections for inner-shell excitations.     

The effect of atomic and extra-atomic relaxation on atomic binding energies

An equivalent-cores-relaxation model is given for calculating atomic binding energies from orbital energies using only ground-state atomic properties. The agreement with experiment is excellent for the noble gases. On the basis of present knowledge of atomic relaxation, the phenomenon of “extra-atomic relaxation”, in which electronic charge is attracted toward a hole-state atom, is shown to have an important effect in lowering atomic core-level binding energies in condensed phases. This will affect the interpretation of most core-level binding energies measured to date.     

Cooperative atomic displacements and melting at the limit of superheating

This paper shows how the melting of superheated crystals originates from the localization of thermal disorder in excited regions of the crystalline structure. Within such regions, disordered thermal motion is found to induce the formation of bulk topological defects. These consist of atoms with a number of nearest neighbors different from the equilibrium one. Such defectively coordinated atoms arrange according to pseudolinear clusters, the number and size of which depend on temperature. Characterized by high mobility, defective atoms and their nearest neighbors are seen to undergo a cooperative dynamics that can result in net atom displacements between equilibrium lattice sites.     

Calculation of the rates of atomic reactions at low energies

The theory of binary atomic reactions is discussed. The matrix Schrödinger equation in the space of electron channels is used for the wave functions of the relative motion of the nuclei; this gives the corresponding quasiclassical equation by retention of terms linear in . Criterion (10) applies for quasiclassical nuclear motion. The additional restriction (13) causes the quasiclassical matrix equation (9) to go over to the basic equation (15) in the method of the central parameter, which indicates the region of application of that method. An Algol-60 program has been drawn up for calculating the rates of atomic reactions via the central-parameter or quasiclassical methods.     

Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters

The accurate first-principles calculation of relative energies of transition metal complexes and clusters is still one of the great challenges for quantum chemistry. Dense lying electronic states and near degeneracies make accurate predictions difficult, and multireference methods with large active spaces are required. Often density functional theory calculations are employed for feasibility reasons, but their actual accuracy for a given system is usually difficult to assess (also because accurate ab initio reference data are lacking). In this work we study the performance of the density matrix renormalization group algorithm for the prediction of relative energies of transition metal complexes and clusters of different spin and molecular structure. In particular, the focus is on the relative energetical order of electronic states of different spin for mononuclear complexes and on the relative energy of different isomers of dinuclear oxo-bridged copper clusters.     

Related upper and lower bounds to atomic binding energies

The method proposed by Singh for the calculations of lower bounds to atomic binding energies has been generalized to encompass upper bounds as well. The result is a pair of related matrix eigenvalue problems, constructed from similar sets of basic matrix elements, with the solution of one yielding the tower bound, and of the other, the upper bound. The upper bounds are identical to those calculated by the Rayleigh–Ritz method, which can be useful when the inversion of the normalization matrix is ill-conditioned. The lower bounds are comparable with the best available in the literature. © 1993 John Wiley & Sons, Inc.     

Lower bound problems and bounds to atomic ionization energies

A simple extension of a method by Calogero and Marchioro for constructing lower bound problems for ground states of systems of indistinguishable particles is applied to atomic systems. Their method is extended to yield an improved lower bound problem, which raises the ground‐state estimate and yields nontrivial lower bounds to excited states that were previously inaccessible by their method. Rigorous upper bounds to atomic ionization energies are also derived. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 779–784, 2000     

On the relation between the formal atomic charges and total molecular energies

It is shown that the total SCF molecular energies are fairly well reproduced by the sum of electrostatic potentials exerted on the nuclei calculated in the point-charge approximation. Hence, there is a very simple relation between the total energies and formal atomic charges in molecules. The semiempirical SCC-MO charges have the same performance as the ab initio DZ ones.     

Revisiting the extrapolation of correlation energies to complete basis set limit

The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double‐zeta (DZ) and triple‐zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian‐3X and Gaussian‐2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts. © 2015 Wiley Periodicals, Inc.     

Perturbation calculation of atomic correlation energies for the first transition period

Results are presented for calculations of Hartree—Fock and correlation energies for the 3dⁿ 4s² and 3dⁿ⁺¹ 4s ground and excited states of the first transition series atoms using second-order Møller—Plesset perturbation theory starting with an unrestricted Hartree—Fock wavefunction.     

Ground-state energies of atomic chains in superstrong magnetic fields

The ground-state energies of hydrogenic and helium chains in superstrong magnetic fields (B ≈? 10⁷?10⁹ Tesla) have been calculated within the single-particle scheme of a heuristic density functional method. Applying the local density approximation (LDA ), the simple Dirac exchange functional was used neglecting correlation effects. The equations were solved iteratively using a basis set of Landau functions in the transverse directions and directly integrating along the longitudinal direction. We obtained binding lengths and, by comparing the binding energies of the chains with the ground-state energies of single atoms, we found condensation energies. © 1995 John Wiley & Sons, Inc.     

Thermochemical data from ab initio calculations. I. Estimation of SCF energies for augmented basis sets and Hartree–Fock limit energies

A procedure is outlined which allows an estimation of molecular energies both for a finite basis set including polarization functions and for the Hartree–Fock limit. It is shown that the orbital error of a given minimal basis is covered to a certain relatively constant percentage by an augmented basis set calculation. Thus an improvement factor Q_av can be determined by analyzing the corresponding results of small molecules where reasonable estimates of HF limit energies can be taken from the literature. For a combination of Pople's STO -3G and 6-31G* basis sets Q_av turns out to be 0.955.     

The prediction of atomic kinetic energies from coordinates of surrounding atoms using kriging machine learning

A novel design of a next-generation force field considers not only the electronic inter-atomic energy but also intra-atomic energy. This strategy promises a faithful mapping between the force field and the quantum mechanics that underpins it. Quantum chemical topology provides an energy partitioning in which atoms have well-defined electronic kinetic energies, and we are interested in capturing how they respond to changes in the positions of surrounding atoms. A machine learning method called kriging successfully creates models from a training set of molecular configurations that can then be used to predict the atomic kinetic energies occurring in previously unseen molecular configurations. We present a proof-of-concept based on four molecules of increasing complexity (methanol, N-methylacetamide, glycine and triglycine). We test how well the atomic kinetic energies can be modelled with respect to training set size, molecule size and elemental composition. For all atoms tested, the mean atomic kinetic energy errors fall below 1.5 kJ mol^?1, and far below this in most cases. This represents errors all under 0.5 % and thus the kinetic energies are well modelled using the kriging method, even when using modest-to-small training set sizes.     

Estimating the temperature dependence of peptide folding entropies and free enthalpies from total energies in molecular dynamics simulations

The temperature dependence of thermodynamic quantities, such as heat capacity, entropy and free enthalpy, may be obtained by using well-known equations that relate these quantities to the enthalpy of the molecular system of interest at a range of temperatures. In turn, the enthalpy of a molecular system can be estimated from molecular dynamics simulations of an appropriate model. To demonstrate this, we have investigated the temperature dependence of the enthalpy, heat capacity, entropy and free enthalpy of a system that consists of a beta-heptapeptide in methanol and have used the statistical mechanics relationships to describe the thermodynamics of the folding/unfolding equilibrium of the peptide. The results illustrate the power of current molecular simulation force fields and techniques in establishing the link between thermodynamic quantities and conformational distributions.     

Basis set dependence of correlation corrections to protonation energies

The protonation energies of NH₃ and H₂O have been computed using a variety of basis sets. It is found that the effect of election correlation on these energies cannot reliably be determined without the use of large (triple-split and polarized) basis sets.     

Communication: Ionization potentials in the limit of large atomic number

By extrapolating the energies of nonrelativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row of the periodic table, even as Z → ∞. The local density approximation for the exchange contribution becomes more accurate (or even exact) in this limit. Extended Thomas-Fermi theory matches the shell average of both the ionization potential and density change.